Xampling: Signal Acquisition and Processing in Union of Subspaces

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio

Quantum Detection with Unknown States

We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown state. We investigate two criteria for optimality. The first is minimization of the worst-case probability of a detection error. For the second we assume a probability distribution on the unknown states, and minimize of the expected probability of a detection error. We find that under both criteria, the optimal detectors are equivalent to the optimal detectors of an ``effective ensemble''. In the worst-case, the effective ensemble is comprised of the known states with altered prior probabilities, and in the average case it is made up of altered states with the original prior probabilities.Comment: Refereed version. Improved numerical examples and figures. A few typos fixe

Meshulami v. Chief Rabbinate of Israel

The Supreme Court addressed a petition to order the Chief Rabbinate to intercalate the Hebrew calendar. The Petitioner sought to delay Passover by thirty days due to the coronavirus pandemic. The Court (per Justice N. Sohlberg, Justices U. Vogelman and Y. Elron concurring) dismissed the petition in limine, expressing doubt as to the justiciability of the issue – a doctrine rarely invoked by the Court – and for lack of cause

Yedidya Loewenthal, Adv. v. Prime Minister

This petition was submitted by four lawyers, residents of Bnei Brak, requesting an order nisi requiring that the State explain why Government Decision declaring the Bnei Brak municipal district as a “restricted zone” for six days not be revoked. The Petitioners argued that the declaration of Bnei Brak as a “restricted zone” was intended only to prevent the spread of the virus to adjacent cities, but in no way related to the prevention of its spread among the residents of Bnei Brak themselves. They further argued that the declaration mortally harms the residents’ freedom of occupation, their liberty, dignity and their freedom of movement, and described the situation as “collective punishment”. The Petitioners argued that the declaration was made “contrary to the obligatory constitutional norms”, that its provisions violate the International Covenant on Civil and Political Rights, that the provisions should have been established in primary legislation, and that the declaration did not meet the tests of proportionality. Lastly, they argued that the declaration was made without public debate, without sufficient evidentiary grounds, and in violation of the right to be heard. Held (per Justice I Amit, Justice A. Baron, Justice Y. Elron concurring): 1. In order to contend with the situation created by the coronavirus epidemic, the Israeli Government exercised its authority under sec. 39 of Basic Law: The Government, and promulgated emergency regulations in regard to a number of subjects intended to mitigate the danger of the spreading of the virus. On April 2, 2020, the Israeli Government decided to promulgate Emergency Regulations (Novel Coronavirus) (Restricted Zone), 5780-2020 (hereinafter: the Regulations). Under sec. 2 (a) of those Regulations: If the coronavirus has significantly spread in a particular are in Israel, and the Ministerial Committee is convinced of the need for restricting entry and exit therefrom in order to prevent the spread of the illness outside the said area, it may, with the consent of the Government, declare the area a restricted zone, on the condition that during the period when the declaration is in force, there will be anappropriate supply of necessary goods and services in the area. 2. In terms of authority, the promulgation of the Regulations is facially in accordance with the Governments’ authority under sec. 39 of Basic Law: The Government, subject to the various limitations as established by law and precedent. 3. The declaration of Bnei Brak as a “restricted zone” followed a large number of incidents of infection in the city, and the fear of an unrestrained transmission of the virus. 4. The expert epidemiological opinion of the Deputy Director of the Public Health Service in the Ministry of Health set out the criteria for establishing a restricted zone subject to additional limitations, which are: a high level of incidence relative to other areas; a significantly higher level of incidence that in the general population; high population density; and clear concentrations of respiratory ailment in the area in the report of the Israeli Center for Disease Control (hereinafter: ICDC). The position of the opinion’s author was that in weighing the data, “the city of Bnei Brak currently constitutes an exceptionally significant center of illness, which will undermine the national effort to lessen the coefficient of contagion”. It was noted that the city of Bnei Brak meets all of the criteria for establishing a restricted zone, and accordingly, severe restrictions upon movement must be imposed. 5. It is settled law that when the Court reviews a decision by a governmental agency, it does not presume to stand in its shoes and make decisions for it in its area of expertise. It is not the practice of the Court to intervene in matters of the agency’s policy, and this is particularly so in regard to policy that is based upon clearly professional data and where the decision is of a clearly professional nature under the agency’s authority and expertise. This is particularly the case in regard to professional matters concerning public health. While the case does not concern a regular administrative decision, but rather a Government decision by virtue of emergency regulations, it is a clearly professional matter. 6. Clearly, the declaration of Bnei Brak as a restricted zone involves a number of violations of basic rights. The purpose of the severe restrictions imposed upon the city’s residents is clear – protecting the health and lives of the city’s residents and the residents of the entire State of Israel. In accordance with the professional discretion, and the data available to the decisionmakers – the scope of illness in the city, the rate of infection, and the population density – there was no recourse but to declare the city of Bnei Brak a “restricted zone”, and thus the declaration was made for a proper purpose. 7. There is a clear rational connection between the means and the purpose. 8. The less harmful means test examines the matter on a metaphoric ladder: was it possible to adopt a “lower” rung on the ladder that would be less harmful to the right? In the present case, there is no denying that declaring the city of Bnai Brak as a “restricted zone” is a very high rung on the ladder. However, it is not sufficient to show that there is another means that would violate the right to a lesser degree. The requirement is that means to achieve the purpose do so in an appropriate and necessary manner. The means were adopted after less harmful means, of the type imposed on the general population, were imposed but did not yield the desired results. In view of the number of people infected and the rate of transmission, and against the background of the city’s extreme density, there were no less harmful means available that could provide the necessary response for stemming the spread of the virus outside the Bnei Brak area at this time. Thus, the second subtest was met. 9. In regard to the proportionality stricto sensu test, the Court can only rely upon the professionals, who are of the opinion that there was no recourse but to impose declare a “restricted zone” in order to stem the spread of the virus. 10. We face an unprecedented situation of fear of the rapid spread of the coronavirus, with all that portends in terms of morbidity, death, and the collapse of the health system. In the horizontal balancing of rights, we now place the violation of fundamental liberties and rights like freedom of movement against the right to life and physical integrity – an uncommon situation in our state. In that horizontal balance, the right to life prevails

Hiddush – For Religious Freedom and Equality v. Israel Defense Forces

[This abstract is not part of the Court\u27s opinion and is provided for the reader\u27s convenience. It has been translated from a Hebrew version prepared by Nevo Press Ltd. and is used with its kind permission.] This petition challenged the policy of the Israel Defense Forces in the matter of military funerals. The petition argued that the bereaved family of a soldier is given a choice between an Orthodox religious military funeral or a civilian funeral, but there is no option for a civilian funeral or a non-Orthodox religious funeral with military honors. The Military Cemeteries Law establishes the right of every fallen IDF soldier to be buried in a military or non-military cemetery, as his relatives may choose, but is silent in regard to the character of the funeral. Therefore, military funerals are primarily regulated by the General Staff Orders (hereinafter: the Order) and directives of the Ministry of Defense. As of the date of the filing of the petition, the Order allowed for the burial of a soldier in one of two ways: a military, Orthodox-religious ceremony in a military cemetery, or a civil ceremony in a civilian cemetery, without any military characteristics. Following the filing of the petition, the Order was amended to permit deviating from the religious characteristics in a military funeral in a military cemetery, as well as for holding a military funeral in a civilian cemetery. Further discussions between the parties led to the additional amending of the Order such that the default would be that changes in the format of the ceremony set out in the Order would be permitted, so that the funeral ceremony would be consistent with the expectations of the family, and would take their feelings into consideration. The Respondent later agreed that in the course of coordinating a funeral, the bereaved family would be informed that its loved one could be buried in a military funeral that would be consistent with its lifestyle and beliefs. In that framework, the family would be permitted to choose whether it desired religious elements in the ceremony, and would be permitted to make other changes “as long as the structure of the ceremony is preserved” and there would be no “desecration of the sanctity of the cemetery”. In view of the changes to the Order agreed to by the Respondent, which granted all of the requested remedies, the Petitioner agreed to withdraw the petition. In dismissing the petition, the Court awarded costs to the Petitioner in recognition of its contribution to advancing the matter

Tbeish v. Attorney General

The Petitioner claimed that he was tortured in the course of interrogation by the Israel Security Agency (ISA) (formerly the General Security Service (GSS)), and petitioned the Court to order the Attorney General to rescind his decision not to open a criminal investigation of the interrogators, and to annul the Attorney General’s guidelines entitled: “ISA Interrogations and the Necessity Defense – Framework for the Attorney General’s Discretion” (hereinafter: the AG’s Guidelines) that provide the basis for the Internal Guidelines of the ISA (hereinafter: the Guidelines). The Petitioners argued that the Guidelines unlawfully permit interrogators to consult with more senior officials in regard to employing “special means” in the course of interrogations. Facts: The Petitioner was interrogated by the Israel Security Service on the suspicion of hostile terrorist activity in the military wing of the Hamas. According to intelligence, the Petitioner knew the location of a substantial arms cache that had been used in the perpetration of several terrorist attacks. Additionally, there was a suspicion that the terrorist network of which the Petitioner was a member, intended to carry out another terrorist attack with those weapons. In light of the Petitioner’s denial of the suspicions, and in view of the ISA interrogators’ opinion that he had information about a planned attack that would endanger human lives, the ISA employed what the Respondents termed “special means of interrogation” against the Petitioner. In the course of his interrogation, the Petitioner provided information about weapons that he had received and had transferred to other Hamas activists, as well as information that aided in the interrogation of other members of the terrorist network, one of whom admitted to planning a kidnapping attack and to “setting in motion additional terrorist activity. Upon conclusion of the investigation, an information was filed against the Petitioner in the Military Court in Judea. The Petitioner pled guilty under a plea agreement, and was convicted of membership and activity in an unlawful association and of commerce in military ordnance. While the case was pending in the trial court, the Petitioner filed a complaint asking that the Attorney General immediately open a criminal investigation against the Petitioner’s interrogators, and against the members of the Prison Service’s medical staff. The Petitioner’s complaint was sent to the Department for Complaints Against the Israel Security Agency. The findings of the Department were sent to the Director responsible for Complaints against the Israel Security Agency in the State Attorney’s Office, who – with the approval of the Attorney General and the State Attorney – decided to close the investigation in regard to the Petitioner’s complaint because she was of the opinion that the investigation’s findings did not justify criminal, disciplinary, or other proceedings against the interrogators. Held: The prosecution enjoys broad discretion in deciding upon the opening of an investigation and in deciding upon filing criminal charges. It is decided law that the Court does not intervene in the manner of the exercise of that discretion, except in exceptional cases in which it is convinced of a substantive flaw in the exercise of discretion or the resulting decision. Evaluating the adequacy of the evidence is distinctively a matter for the expertise of the prosecution. Therefore, intervention into a decision not to open an investigation for lack of adequate evidence is even more restricted. Examining the reasonableness of the decision must be in accordance with the criteria of the Court in regard to the authority of ISA interrogators to employ physical means of interrogation and the circumstances in which such means may be permitted. Prior to the Court’s decision in HCJ 5100/94 Public Committee against Torture v. State of Israel, the necessity defense formed the basis for the ISA guidelines in regard to the use of interrogation methods that, in the absence of any alternative, permitted the use of physical means where necessary to save human life. Those guidelines were declared unlawful and void in HCJ 5100/94. However, that decision also comprised two holdings of importance to the matters addressed by this petition. It was held that the necessity defense might be available to an interrogator who employed physical means of interrogation in “ticking bomb” circumstances, and who was subsequently charged with an offense. It was further held that the demand for “immediacy” under sec. 34K of the Penal Law refers to the imminent nature of the act rather than of the danger. Thus, the imminence criteria is satisfied even if the threat will be realized in a few days, or even in a few weeks, provided that it is certain to materialize and there is no alternative means of preventing it. It was further held that guidelines for the use of physical force in interrogations must be based upon express authority under statute, and not upon defenses to criminal responsibility. No general authority could be founded upon the necessity defense alone. However, the Court added: “The Attorney General can instruct himself regarding circumstances in which investigators shall not stand trial, if they claim to have acted from ‘necessity’”. The circumstances of the Petitioner’s interrogation clearly show that the interrogation was intended to prevent a concrete threat to human life of a high degree of certainty. There was no alternative to the means employed for obtaining the information. Those means were proportionate to the severity of the threat they were meant to prevent. The Director’s finding that the use of those means falls within the scope of the necessity defense was grounded. The Petitioner’s claim that resort can only be made to the necessity defense in the course of a trial lacks systematic logic and is contrary to the efficient and proper administration of criminal proceedings. Where the prosecution is convinced that a suspect can claim necessity, there is no justification for conducting criminal proceedings that will lead to a result that is clear from the outset. The Attorney General’s Directives and the ISA’s classified internal guidelines do not contradict what was held in HCJ 5100/94

Examining the direct and indirect effect that individual and contextual risk factors have in predicting substance abuse

Substance abuse levels in South Africa have continued to rise, with the age of first experimentation with drugs reported as being 10 years. Several studies have shown that substance abuse has an adverse impact on users, their families and their communities, resulting in a number of social, psychological and economic struggles. Moreover, substance abuse places an increased psychological, social and financial burden on the individual and the family, as it has been related to the destabilisation of the nuclear and extended family units, permeating every area of life and affecting the very social fabric of society. This study therefore endeavoured to determine which of the individual and contextual risk factors measured by the South African Substance Use Contextual Risk Instrument (SASUCRI) best predicts substance abuse in a sample of self-identified substance abusers. Additionally, the study sought to determine the magnitude, strength and direction of the interaction of the individual and contextual risk factors in predicting substance abuse. The specific aims of the study were: 1) to build a theoretical model that best approximates the identified and measured individual and contextual factors associated with substance abuse, 2) to use structural equation modelling (SEM) to test the adequacy of the model’s fit to the data that have been collected, 3) to use SEM to statistically determine which of the perceived individual or contextual factors best predict substance abuse, and 4) to use SEM to statistically determine which combination of perceived individual and contextual factors best predict substance abuse. To achieve these aims, the study applied SEM to data collected from individuals seeking either inpatient or outpatient treatment for substance abuse in the Eastern Cape and Western Cape Provinces of South Africa, respectively. The purpose of SEM is to a priori specify a theoretical causal model consisting of a set of predicted covariances between variables, and then test whether it is plausible when compared to the observed data. The appropriateness of performing SEM exists in its ability and suitability to examine the nature and magnitude of postulated dependence relationships, while simultaneously assessing the direct and indirect relations of the variables. The theoretical causal model that was tested contained latent and manifest variables that were identified as risk factors for substance abuse. The causal model was informed by Bronfenbrenner’s (1977a, 1986) ecological systems theory (EST) and was specified to approximate the different systems of the theory. Data for the study were collected using the relatively newly developed and validated SASUCRI. The results of the confirmatory factor analysis (CFA) showed that the SASUCRI was a reliable and valid instrument to use with this population, and that the results of the structural model can be interpreted with confidence. The fit statistics, for the normal theory and related bootstrap latent path SEM, all indicate that the model is an excellent fit to the data CMIN/DF = 2.82, NFI = .946, CFI = .97, RMSEA = .04., thus achieving the study’s objective. The normal theory analysis of the paths in the diagram identified the microsystem, “Access/proximity to drugs” (APTD) and “Concerns for future” (CFF) as significant predictors of substance abuse, whereas the bootstrap analysis of the paths identified the macrosystem, APTD and CFF as significant predictors of substance abuse. This study identified 10 risk profiles that interact in the prediction of substance abuse; these are: individuals with low self-efficacy (SE) who perceive their family as lacking or having low intra-family communication, who lack positive peer support, who perceive criminal behaviours as normal, who feel a strong need to fit in, who are less religious, who have easy access to drugs, who lack a sense of community traditions and belonging, who see public displays of substance use (SU) as normal, and who lack concern for the future, are at 59% greater risk of substance abuse. Though micro level factors (low SE, lack of or low intra-family communication, and a lack of positive peer support) and meso-level factors (normalisation of criminal activity, a strong need to fit in, and being less religious) does not significantly predict abuse, they significantly interact with external factors in predicting substance abuse. Thus, it is only when they interact with factors located in the other systems (exosystem, macrosystem and chronosystem) that they become significant predictors of substance abuse. Conversely, exosystem (easy access to drugs), macrosystem (lack of a sense of community traditions and belonging, commonplace public displays of SU), and chronosystem factors (lack of concern for the future), independently are significant predictors of substance abuse. These findings carry significant public health implications by challenging the prevailing focus on individual-based interventions. Recognising that the drivers of substance abuse extend beyond individual factors, this study therefore advocates for interventions that address the broader systems contributing to the issue. This has the potential to inform more effective and holistic public health strategies. Finally, this study emphasises the need for comprehensive strategies that span different systems, acknowledging the role of family, community and societal factors. This call for complex interventions aligns with the ecological systems perspective, advocating for a paradigm shift in how we address SU by considering the broader environmental influences that contribute to the problem. In summary, this study not only contributes to the academic understanding of SU, but also has practical implications for public health policies and interventions.Thesis (PhD) -- Faculty of Humanities, Psychology, 202

On the use of dexamethasone-loaded liposomes to induce the osteogenic differentiation of human mesenchymal stem cells

Article first published online: 7 Oct. 2013Stem cells have received considerable attention by the scientific community because of their potential for tissue engineering and regenerative medicine. The most frequently used method to promote their differentiation is supplementation of the in vitro culture medium with growth/differentiation factors (GDFs). The limitations of that strategy caused by the short half-life of GDFs limit its efficacy in vivo and consequently its clinical use. Thus, the development of new concepts that enable the bioactivity and bioavailability of GDFs to be protected, both in vitro and in vivo, is very relevant. Nanoparticle-based drug delivery systems can be injected, protect the GDFs and enable spatiotemporal release kinetics to be controlled. Liposomes are well-established nanodelivery devices presenting significant advantages, viz. a high load-carrying capacity, relative safety and easy production, and a versatile nature in terms of possible formulations and surface functionalization. The main objective of the present study was to optimize the formulation of liposomes to encapsulate dexamethasone (Dex). Our results showed that the optimized Dex-loaded liposomes do not have any cytotoxic effect on human bone marrow-derived mesenchymal stem cells (hBMSCs). More importantly, they were able to promote an earlier induction of differentiation of hBMSCs into the osteogenic lineage, as demonstrated by the expression of osteoblastic markers, both phenotypically and genotypically. We concluded that Dex-loaded liposomes represent a viable nanoparticle strategy with enhanced safety and efficacy for tissue engineering and regenerative medicine.The authors thank the Portuguese Foundation for Science and Technology for a PhD grant (No. SFRH/BD/62465/2009, to N. S. Monteiro). This work was partly supported by the FIND and BIND Project (No. NMP4-SL-2009-229292) and the OsteoGraphy Project (No. PTDC/EME-MFE/2008)